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1/* $OpenBSD: bn_div.c,v 1.41 2024/04/10 14:58:06 beck Exp $ */
2/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
3 * All rights reserved.
4 *
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
8 *
9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to. The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
15 *
16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
22 *
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
25 * are met:
26 * 1. Redistributions of source code must retain the copyright
27 * notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 * notice, this list of conditions and the following disclaimer in the
30 * documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 * must display the following acknowledgement:
33 * "This product includes cryptographic software written by
34 * Eric Young (eay@cryptsoft.com)"
35 * The word 'cryptographic' can be left out if the rouines from the library
36 * being used are not cryptographic related :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
40 *
41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
51 * SUCH DAMAGE.
52 *
53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed. i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
57 */
58
59#include <assert.h>
60#include <stdio.h>
61
62#include <openssl/opensslconf.h>
63
64#include <openssl/bn.h>
65#include <openssl/err.h>
66
67#include "bn_arch.h"
68#include "bn_local.h"
69#include "bn_internal.h"
70
71BN_ULONG bn_div_3_words(const BN_ULONG *m, BN_ULONG d1, BN_ULONG d0);
72
73#ifndef HAVE_BN_DIV_WORDS
74#if defined(BN_LLONG) && defined(BN_DIV2W)
75
76BN_ULONG
77bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d)
78{
79 return ((BN_ULONG)(((((BN_ULLONG)h) << BN_BITS2)|l)/(BN_ULLONG)d));
80}
81
82#else
83
84/* Divide h,l by d and return the result. */
85/* I need to test this some more :-( */
86BN_ULONG
87bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d)
88{
89 BN_ULONG dh, dl, q,ret = 0, th, tl, t;
90 int i, count = 2;
91
92 if (d == 0)
93 return (BN_MASK2);
94
95 i = BN_num_bits_word(d);
96 assert((i == BN_BITS2) || (h <= (BN_ULONG)1 << i));
97
98 i = BN_BITS2 - i;
99 if (h >= d)
100 h -= d;
101
102 if (i) {
103 d <<= i;
104 h = (h << i) | (l >> (BN_BITS2 - i));
105 l <<= i;
106 }
107 dh = (d & BN_MASK2h) >> BN_BITS4;
108 dl = (d & BN_MASK2l);
109 for (;;) {
110 if ((h >> BN_BITS4) == dh)
111 q = BN_MASK2l;
112 else
113 q = h / dh;
114
115 th = q * dh;
116 tl = dl * q;
117 for (;;) {
118 t = h - th;
119 if ((t & BN_MASK2h) ||
120 ((tl) <= (
121 (t << BN_BITS4) |
122 ((l & BN_MASK2h) >> BN_BITS4))))
123 break;
124 q--;
125 th -= dh;
126 tl -= dl;
127 }
128 t = (tl >> BN_BITS4);
129 tl = (tl << BN_BITS4) & BN_MASK2h;
130 th += t;
131
132 if (l < tl)
133 th++;
134 l -= tl;
135 if (h < th) {
136 h += d;
137 q--;
138 }
139 h -= th;
140
141 if (--count == 0)
142 break;
143
144 ret = q << BN_BITS4;
145 h = ((h << BN_BITS4) | (l >> BN_BITS4)) & BN_MASK2;
146 l = (l & BN_MASK2l) << BN_BITS4;
147 }
148 ret |= q;
149 return (ret);
150}
151#endif /* !defined(BN_LLONG) && defined(BN_DIV2W) */
152#endif
153
154/*
155 * Divide a double word (h:l) by d, returning the quotient q and the remainder
156 * r, such that q * d + r is equal to the numerator.
157 */
158#ifndef HAVE_BN_DIV_REM_WORDS
159#ifndef HAVE_BN_DIV_REM_WORDS_INLINE
160static inline void
161bn_div_rem_words_inline(BN_ULONG h, BN_ULONG l, BN_ULONG d, BN_ULONG *out_q,
162 BN_ULONG *out_r)
163{
164 BN_ULONG q, r;
165
166 q = bn_div_words(h, l, d);
167 r = (l - q * d) & BN_MASK2;
168
169 *out_q = q;
170 *out_r = r;
171}
172#endif
173
174void
175bn_div_rem_words(BN_ULONG h, BN_ULONG l, BN_ULONG d, BN_ULONG *out_q,
176 BN_ULONG *out_r)
177{
178 bn_div_rem_words_inline(h, l, d, out_q, out_r);
179}
180#endif
181
182#ifndef HAVE_BN_DIV_3_WORDS
183
184/*
185 * Interface is somewhat quirky, |m| is pointer to most significant limb,
186 * and less significant limb is referred at |m[-1]|. This means that caller
187 * is responsible for ensuring that |m[-1]| is valid. Second condition that
188 * has to be met is that |d0|'s most significant bit has to be set. Or in
189 * other words divisor has to be "bit-aligned to the left." The subroutine
190 * considers four limbs, two of which are "overlapping," hence the name...
191 */
192BN_ULONG
193bn_div_3_words(const BN_ULONG *m, BN_ULONG d1, BN_ULONG d0)
194{
195 BN_ULONG n0, n1, q, t2h, t2l;
196 BN_ULONG rem = 0;
197
198 n0 = m[0];
199 n1 = m[-1];
200
201 if (n0 == d0)
202 return BN_MASK2;
203
204 /* n0 < d0 */
205 bn_div_rem_words(n0, n1, d0, &q, &rem);
206
207 bn_mulw(d1, q, &t2h, &t2l);
208
209 for (;;) {
210 if (t2h < rem || (t2h == rem && t2l <= m[-2]))
211 break;
212 q--;
213 rem += d0;
214 if (rem < d0)
215 break; /* don't let rem overflow */
216 if (t2l < d1)
217 t2h--;
218 t2l -= d1;
219 }
220
221 return q;
222}
223#endif /* !HAVE_BN_DIV_3_WORDS */
224
225/*
226 * BN_div_internal computes quotient := numerator / divisor, rounding towards
227 * zero and setting remainder such that quotient * divisor + remainder equals
228 * the numerator. Thus:
229 *
230 * quotient->neg == numerator->neg ^ divisor->neg (unless result is zero)
231 * remainder->neg == numerator->neg (unless the remainder is zero)
232 *
233 * If either the quotient or remainder is NULL, the respective value is not
234 * returned.
235 */
236static int
237BN_div_internal(BIGNUM *quotient, BIGNUM *remainder, const BIGNUM *numerator,
238 const BIGNUM *divisor, BN_CTX *ctx, int ct)
239{
240 int norm_shift, i, loop, r_neg;
241 BIGNUM *tmp, wnum, *snum, *sdiv, *res;
242 BN_ULONG *resp, *wnump;
243 BN_ULONG d0, d1;
244 int num_n, div_n;
245 int no_branch = 0;
246 int ret = 0;
247
248 BN_CTX_start(ctx);
249
250 /* Invalid zero-padding would have particularly bad consequences. */
251 if (numerator->top > 0 && numerator->d[numerator->top - 1] == 0) {
252 BNerror(BN_R_NOT_INITIALIZED);
253 goto err;
254 }
255
256 if (ct)
257 no_branch = 1;
258
259 if (BN_is_zero(divisor)) {
260 BNerror(BN_R_DIV_BY_ZERO);
261 goto err;
262 }
263
264 if (!no_branch) {
265 if (BN_ucmp(numerator, divisor) < 0) {
266 if (remainder != NULL) {
267 if (!bn_copy(remainder, numerator))
268 goto err;
269 }
270 if (quotient != NULL)
271 BN_zero(quotient);
272
273 goto done;
274 }
275 }
276
277 if ((tmp = BN_CTX_get(ctx)) == NULL)
278 goto err;
279 if ((snum = BN_CTX_get(ctx)) == NULL)
280 goto err;
281 if ((sdiv = BN_CTX_get(ctx)) == NULL)
282 goto err;
283 if ((res = quotient) == NULL) {
284 if ((res = BN_CTX_get(ctx)) == NULL)
285 goto err;
286 }
287
288 /* First we normalise the numbers. */
289 norm_shift = BN_BITS2 - BN_num_bits(divisor) % BN_BITS2;
290 if (!BN_lshift(sdiv, divisor, norm_shift))
291 goto err;
292 sdiv->neg = 0;
293 norm_shift += BN_BITS2;
294 if (!BN_lshift(snum, numerator, norm_shift))
295 goto err;
296 snum->neg = 0;
297
298 if (no_branch) {
299 /*
300 * Since we don't know whether snum is larger than sdiv, we pad
301 * snum with enough zeroes without changing its value.
302 */
303 if (snum->top <= sdiv->top + 1) {
304 if (!bn_wexpand(snum, sdiv->top + 2))
305 goto err;
306 for (i = snum->top; i < sdiv->top + 2; i++)
307 snum->d[i] = 0;
308 snum->top = sdiv->top + 2;
309 } else {
310 if (!bn_wexpand(snum, snum->top + 1))
311 goto err;
312 snum->d[snum->top] = 0;
313 snum->top++;
314 }
315 }
316
317 div_n = sdiv->top;
318 num_n = snum->top;
319 loop = num_n - div_n;
320
321 /*
322 * Setup a 'window' into snum - this is the part that corresponds to the
323 * current 'area' being divided.
324 */
325 wnum.neg = 0;
326 wnum.d = &(snum->d[loop]);
327 wnum.top = div_n;
328 /* only needed when BN_ucmp messes up the values between top and max */
329 wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
330 wnum.flags = snum->flags | BN_FLG_STATIC_DATA;
331
332 /* Get the top 2 words of sdiv */
333 /* div_n=sdiv->top; */
334 d0 = sdiv->d[div_n - 1];
335 d1 = (div_n == 1) ? 0 : sdiv->d[div_n - 2];
336
337 /* pointer to the 'top' of snum */
338 wnump = &(snum->d[num_n - 1]);
339
340 /* Setup to 'res' */
341 if (!bn_wexpand(res, (loop + 1)))
342 goto err;
343 res->top = loop - no_branch;
344 r_neg = numerator->neg ^ divisor->neg;
345 resp = &(res->d[loop - 1]);
346
347 /* space for temp */
348 if (!bn_wexpand(tmp, (div_n + 1)))
349 goto err;
350
351 if (!no_branch) {
352 if (BN_ucmp(&wnum, sdiv) >= 0) {
353 bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
354 *resp = 1;
355 } else
356 res->top--;
357 }
358
359 /*
360 * If res->top == 0 then clear the neg value otherwise decrease the resp
361 * pointer.
362 */
363 if (res->top == 0)
364 res->neg = 0;
365 else
366 resp--;
367
368 for (i = 0; i < loop - 1; i++, wnump--, resp--) {
369 BN_ULONG q, l0;
370
371 /*
372 * The first part of the loop uses the top two words of snum and
373 * sdiv to calculate a BN_ULONG q such that:
374 *
375 * | wnum - sdiv * q | < sdiv
376 */
377 q = bn_div_3_words(wnump, d1, d0);
378 l0 = bn_mul_words(tmp->d, sdiv->d, div_n, q);
379 tmp->d[div_n] = l0;
380 wnum.d--;
381
382 /*
383 * Ignore top values of the bignums just sub the two BN_ULONG
384 * arrays with bn_sub_words.
385 */
386 if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n + 1)) {
387 /*
388 * Note: As we have considered only the leading two
389 * BN_ULONGs in the calculation of q, sdiv * q might be
390 * greater than wnum (but then (q-1) * sdiv is less or
391 * equal than wnum).
392 */
393 q--;
394 if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n)) {
395 /*
396 * We can't have an overflow here (assuming
397 * that q != 0, but if q == 0 then tmp is
398 * zero anyway).
399 */
400 (*wnump)++;
401 }
402 }
403 /* store part of the result */
404 *resp = q;
405 }
406
407 bn_correct_top(snum);
408
409 if (remainder != NULL) {
410 /*
411 * Keep a copy of the neg flag in numerator because if
412 * remainder == numerator, BN_rshift() will overwrite it.
413 */
414 int neg = numerator->neg;
415
416 BN_rshift(remainder, snum, norm_shift);
417 BN_set_negative(remainder, neg);
418 }
419
420 if (no_branch)
421 bn_correct_top(res);
422
423 BN_set_negative(res, r_neg);
424
425 done:
426 ret = 1;
427 err:
428 BN_CTX_end(ctx);
429
430 return ret;
431}
432
433int
434BN_div(BIGNUM *quotient, BIGNUM *remainder, const BIGNUM *numerator,
435 const BIGNUM *divisor, BN_CTX *ctx)
436{
437 int ct;
438
439 ct = BN_get_flags(numerator, BN_FLG_CONSTTIME) != 0 ||
440 BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0;
441
442 return BN_div_internal(quotient, remainder, numerator, divisor, ctx, ct);
443}
444LCRYPTO_ALIAS(BN_div);
445
446int
447BN_div_nonct(BIGNUM *quotient, BIGNUM *remainder, const BIGNUM *numerator,
448 const BIGNUM *divisor, BN_CTX *ctx)
449{
450 return BN_div_internal(quotient, remainder, numerator, divisor, ctx, 0);
451}
452
453int
454BN_div_ct(BIGNUM *quotient, BIGNUM *remainder, const BIGNUM *numerator,
455 const BIGNUM *divisor, BN_CTX *ctx)
456{
457 return BN_div_internal(quotient, remainder, numerator, divisor, ctx, 1);
458}
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